Tumor evolution project

Data used

In this notebook, we are using the tmb_genomic.tsv file generated from the 01-preprocess-data.Rmd script.

Set up

suppressPackageStartupMessages({
  library(tidyverse)
})

Directories and File Inputs/Outputs

# Detect the \.git\ folder. This will be in the project root directory.
# Use this as the root directory to ensure proper sourcing of functions
# no matter where this is called from.
root_dir <- rprojroot::find_root(rprojroot::has_dir(\.git\))
scratch_dir <- file.path(root_dir, \scratch\)
analysis_dir <- file.path(root_dir, \analyses\, \tmb-vaf-longitudinal\) 
input_dir <- file.path(analysis_dir, \input\)

# Input files
tmb_genomic_file <- file.path(scratch_dir, \tmb_genomic.tsv\)
tumor_descriptor_color_palette_file <- file.path(root_dir, \figures\, \palettes\, \tumor_descriptor_color_palette.tsv\)

# File path to plots directory
plots_dir <-
  file.path(analysis_dir, \plots\)
if (!dir.exists(plots_dir)) {
  dir.create(plots_dir)
}

source(paste0(analysis_dir, \/util/function-create-barplot.R\))
source(paste0(analysis_dir, \/util/function-create-dumbbell-plot.R\))
source(paste0(root_dir, \/figures/scripts/theme.R\))

Read in data and process

# Read and process tmb_genomic file
tmb_genomic_total <- readr::read_tsv(tmb_genomic_file, guess_max = 100000, show_col_types = FALSE) 

# Are there any samples with both WGS and WXS? 
tmb_genomic_total %>% 
  unique() %>% 
  arrange(Kids_First_Participant_ID, experimental_strategy)  %>%
  group_by(Kids_First_Participant_ID) %>%
  dplyr::summarise(experimental_strategy_sum = str_c(experimental_strategy, collapse = \;\)) 
# There are, so let's remove these from downstream analyses.
tmb_df_filter <- tmb_genomic_total %>% 
  filter(!experimental_strategy == \WXS\) %>% 
  dplyr:::mutate(patient_id = paste(short_histology, Kids_First_Participant_ID, sep = \_\))
    
# Read color palette
tumor_descriptor_color_palette <- readr::read_tsv(tumor_descriptor_color_palette_file, guess_max = 100000, show_col_types = FALSE)

TMB per Patient case

We will explore TMB per Kids_First_Participant_ID over time by creating stacked barplots.

# Define parameters for function
ylim <- 360

# df
f <- c(\Second Malignancy\, \Unavailable\, \Deceased\, \Recurrence\, \Progressive\, \Diagnosis\) # Level df by timepoints
plot_df <- tmb_df_filter %>% 
  dplyr:::mutate(tumor_descriptor = factor(tumor_descriptor),
                 tumor_descriptor = fct_relevel(tumor_descriptor, f)) 

# Run function
fname <- paste0(plots_dir, \/\, \TMB-genomic-total.pdf\)
print(fname)
[1] \/home/rstudio/pbta-tumor-evolution/CHOP/GitHub/pbta-tumor-evolution/analyses/tmb-vaf-longitudinal/plots/TMB-genomic-total.pdf\
p <- create_stacked_barplot(tmb_df = plot_df, ylim = ylim)

pdf(file = fname, width = 15, height = 6)
print(p)
dev.off()
png 
  2 

Attention: Hypermutant TMB defined as ≥10 Mb, and Ultrahypermutant TMB defined as ≥100 mutations/Mb (https://pubmed.ncbi.nlm.nih.gov/29056344/).

Here, we notice that there are samples with high TMB (hyper-mutant samples). Next, we will exclude these samples (threshold >= 10) from downstream analysis. Attention is needed in cases with high number of mutations in only one timepoint as this will lead to un-matched longitudinal samples. We will also remove those so we always have matched longitudinal samples.

# Filter df
plot_df_filter <- tmb_df_filter %>%
  filter(!tmb >= 10)  %>%
  unique() %>% 
  arrange(Kids_First_Participant_ID, tumor_descriptor) %>%
  group_by(Kids_First_Participant_ID) %>%
  dplyr::summarise(tumor_descriptor_sum = str_c(tumor_descriptor, collapse = \;\)) %>% 
  filter(!tumor_descriptor_sum %in% c(\Diagnosis\, \Progressive\, \Recurrence\)) %>% 
  dplyr::left_join(tmb_df_filter, by = c(\Kids_First_Participant_ID\, \tumor_descriptor_sum\)) %>% 
  mutate(cancer_group_sum = ifelse(short_histology == \HGAT\, \High-grade glioma\,
                                   ifelse(short_histology == \LGAT\, \Low-grade glioma\, \Other cancer group\)),
         cancer_group_sum = replace_na(cancer_group_sum, \Other\),
         tumor_descriptor = factor(tumor_descriptor),
         tumor_descriptor = fct_relevel(tumor_descriptor, f)) %>% 
  drop_na(tmb) 


# Define parameters for function
ylim <- 12.5
plot_df_filter <- plot_df_filter

# Run function
fname <- paste0(plots_dir, \/\, \TMB-genomic-no-hypermutants.pdf\)
print(fname)
[1] \/home/rstudio/pbta-tumor-evolution/CHOP/GitHub/pbta-tumor-evolution/analyses/tmb-vaf-longitudinal/plots/TMB-genomic-no-hypermutants.pdf\
p <- create_stacked_barplot(tmb_df = plot_df_filter, ylim = ylim)

pdf(file = fname, width = 25, height = 8)
print(p)
dev.off()
png 
  2 

TMB across timepoints and cancer types per Patient case

We will explore TMB per cancer group over time by creating dumbbell plots. We classified by using cancer types with the highest number of samples (High- and Low-grade gliomas) versus any other cancer groups.

cancer_groups <- unique(as.character(plot_df_filter$cancer_group_sum))
cancer_groups <- sort(cancer_groups, decreasing = FALSE)
print(cancer_groups)
[1] \High-grade glioma\  \Low-grade glioma\   \Other cancer group\
for (i in seq_along(cancer_groups)) {
  print(i)
  df_ct_sub <- plot_df_filter %>% 
    filter(cancer_group_sum == cancer_groups [i])
  
  if (i == 1) {
    print(cancer_groups [i])
    # Define parameters for function
    ylim <- 8
    } else if (i == 2) {
      print(cancer_groups [i])
      # Define parameters for function
      ylim <- 4
      } else {
        print(cancer_groups [i])
        # Define parameters for function
        ylim <- 4
      }
    
    # Name plots
    fname <- paste0(plots_dir, \/\, \TMB-genomic-dumbbell\, \-\, cancer_groups[i], \.pdf\)
    print(fname)
    
    # Run function
    p <- create_dumbbell_ct(tmb_df = df_ct_sub, 
                                 ylim = ylim, 
                                 ct_id = cancer_groups[i])
    pdf(file = fname, width = 18, height = 10)
    print(p)
    dev.off()
}
[1] 1
[1] \High-grade glioma\
[1] \/home/rstudio/pbta-tumor-evolution/CHOP/GitHub/pbta-tumor-evolution/analyses/tmb-vaf-longitudinal/plots/TMB-genomic-dumbbell-High-grade glioma.pdf\

[1] 2
[1] \Low-grade glioma\
[1] \/home/rstudio/pbta-tumor-evolution/CHOP/GitHub/pbta-tumor-evolution/analyses/tmb-vaf-longitudinal/plots/TMB-genomic-dumbbell-Low-grade glioma.pdf\

[1] 3
[1] \Other cancer group\
[1] \/home/rstudio/pbta-tumor-evolution/CHOP/GitHub/pbta-tumor-evolution/analyses/tmb-vaf-longitudinal/plots/TMB-genomic-dumbbell-Other cancer group.pdf\

Total number of mutations across timepoints and cancer types per Patient case

for (i in seq_along(cancer_groups)) {
  print(i)
  df_ct_sub <- plot_df_filter %>% 
    filter(cancer_group_sum == cancer_groups [i])
  
  if (i == 1) {
    print(cancer_groups [i])
    # Define parameters for function
    ylim <- 260
    } else if (i == 2) {
      print(cancer_groups [i])
      # Define parameters for function
      ylim <- 150
      } else {
        print(cancer_groups [i])
        # Define parameters for function
        ylim <- 150
      }
    
    # Name plots
    fname <- paste0(plots_dir, \/\, \Mutations-genomic-dumbbell\, \-\, cancer_groups[i], \.pdf\)
    print(fname)
    
    # Run function
    p <- create_dumbbell_ct_mut(tmb_df = df_ct_sub, 
                                 ylim = ylim, 
                                 ct_id = cancer_groups[i])
    pdf(file = fname, width = 18, height = 10)
    print(p)
    dev.off()
}
[1] 1
[1] \High-grade glioma\
[1] \/home/rstudio/pbta-tumor-evolution/CHOP/GitHub/pbta-tumor-evolution/analyses/tmb-vaf-longitudinal/plots/Mutations-genomic-dumbbell-High-grade glioma.pdf\

[1] 2
[1] \Low-grade glioma\
[1] \/home/rstudio/pbta-tumor-evolution/CHOP/GitHub/pbta-tumor-evolution/analyses/tmb-vaf-longitudinal/plots/Mutations-genomic-dumbbell-Low-grade glioma.pdf\

[1] 3
[1] \Other cancer group\
[1] \/home/rstudio/pbta-tumor-evolution/CHOP/GitHub/pbta-tumor-evolution/analyses/tmb-vaf-longitudinal/plots/Mutations-genomic-dumbbell-Other cancer group.pdf\

Total number of mutations across timepoints and biospecimen sample per Patient case

Here, we want to explore the number of mutations per timepoint and biospecimen sample per patient case.

samples <- unique(as.character(plot_df_filter$Kids_First_Participant_ID))
print(samples)
 [1] \PT_00G007DM\ \PT_02J5CWN5\ \PT_1H2REHT2\ \PT_1ZAWNGWT\ \PT_25Z2NX27\
 [6] \PT_2ECVKTTQ\ \PT_2FVTD0WR\ \PT_2YT37G8P\ \PT_37B5JRP1\ \PT_3R0P995B\
[11] \PT_3T3VGWC6\ \PT_3VCS1PPF\ \PT_7M2PGCBV\ \PT_82MX6J77\ \PT_89XRZBSG\
[16] \PT_8GN3TQRM\ \PT_962TCBVR\ \PT_98QMQZY7\ \PT_99S5BPE3\ \PT_9PJR0ZK7\
[21] \PT_9S6WMQ92\ \PT_AQWDQW27\ \PT_CXT81GRM\ \PT_DFQAH7RS\ \PT_ESHACWF6\
[26] \PT_FN4GEEFR\ \PT_HFQNKP5X\ \PT_HJMP6PH2\ \PT_JNEV57VK\ \PT_JP1FDKN9\
[31] \PT_JSFBMK5V\ \PT_K8ZV7APT\ \PT_KMHGNCNR\ \PT_MDWPRDBT\ \PT_MNSEJCDM\
[36] \PT_N8W26H19\ \PT_NPETR8RY\ \PT_PFA762TK\ \PT_PR4YBBH3\ \PT_QH9H491G\
[41] \PT_RJ1TJ2KH\ \PT_S2SQJVGK\ \PT_S4YNE17X\ \PT_T2M1338J\ \PT_TKWTTRQ7\
[46] \PT_W6AWJJK7\ \PT_WP871F5S\ \PT_XA98HG1C\ \PT_XHYBZKCX\ \PT_XTVQB9S4\
[51] \PT_YGN06RPZ\ \PT_Z4GS3ZQQ\ \PT_ZMKMKCFQ\ \PT_ZZRBX5JT\
for (i in seq_along(samples)) {
  print(i)
  tmb_sub <- plot_df_filter %>%
    filter(Kids_First_Participant_ID == samples[i])
  
  # Define parameters for function
  ylim <- 260
 
  # Run function
  fname <- paste0(plots_dir, \/\, samples[i], \-TMB-barplot.pdf\)
  print(fname)
  p <- create_barplot_sample(tmb_df = tmb_sub,
                             ylim = ylim,
                             sid = samples[i])
  pdf(file = fname, width = 5, height = 4)
  print(p)
  dev.off()
}
[1] 1
[1] \/home/rstudio/pbta-tumor-evolution/CHOP/GitHub/pbta-tumor-evolution/analyses/tmb-vaf-longitudinal/plots/PT_00G007DM-TMB-barplot.pdf\

[1] 2
[1] \/home/rstudio/pbta-tumor-evolution/CHOP/GitHub/pbta-tumor-evolution/analyses/tmb-vaf-longitudinal/plots/PT_02J5CWN5-TMB-barplot.pdf\

[1] 3
[1] \/home/rstudio/pbta-tumor-evolution/CHOP/GitHub/pbta-tumor-evolution/analyses/tmb-vaf-longitudinal/plots/PT_1H2REHT2-TMB-barplot.pdf\

[1] 4
[1] \/home/rstudio/pbta-tumor-evolution/CHOP/GitHub/pbta-tumor-evolution/analyses/tmb-vaf-longitudinal/plots/PT_1ZAWNGWT-TMB-barplot.pdf\

[1] 5
[1] \/home/rstudio/pbta-tumor-evolution/CHOP/GitHub/pbta-tumor-evolution/analyses/tmb-vaf-longitudinal/plots/PT_25Z2NX27-TMB-barplot.pdf\

[1] 6
[1] \/home/rstudio/pbta-tumor-evolution/CHOP/GitHub/pbta-tumor-evolution/analyses/tmb-vaf-longitudinal/plots/PT_2ECVKTTQ-TMB-barplot.pdf\

[1] 7
[1] \/home/rstudio/pbta-tumor-evolution/CHOP/GitHub/pbta-tumor-evolution/analyses/tmb-vaf-longitudinal/plots/PT_2FVTD0WR-TMB-barplot.pdf\

[1] 8
[1] \/home/rstudio/pbta-tumor-evolution/CHOP/GitHub/pbta-tumor-evolution/analyses/tmb-vaf-longitudinal/plots/PT_2YT37G8P-TMB-barplot.pdf\

[1] 9
[1] \/home/rstudio/pbta-tumor-evolution/CHOP/GitHub/pbta-tumor-evolution/analyses/tmb-vaf-longitudinal/plots/PT_37B5JRP1-TMB-barplot.pdf\

[1] 10
[1] \/home/rstudio/pbta-tumor-evolution/CHOP/GitHub/pbta-tumor-evolution/analyses/tmb-vaf-longitudinal/plots/PT_3R0P995B-TMB-barplot.pdf\

[1] 11
[1] \/home/rstudio/pbta-tumor-evolution/CHOP/GitHub/pbta-tumor-evolution/analyses/tmb-vaf-longitudinal/plots/PT_3T3VGWC6-TMB-barplot.pdf\

[1] 12
[1] \/home/rstudio/pbta-tumor-evolution/CHOP/GitHub/pbta-tumor-evolution/analyses/tmb-vaf-longitudinal/plots/PT_3VCS1PPF-TMB-barplot.pdf\

[1] 13
[1] \/home/rstudio/pbta-tumor-evolution/CHOP/GitHub/pbta-tumor-evolution/analyses/tmb-vaf-longitudinal/plots/PT_7M2PGCBV-TMB-barplot.pdf\

[1] 14
[1] \/home/rstudio/pbta-tumor-evolution/CHOP/GitHub/pbta-tumor-evolution/analyses/tmb-vaf-longitudinal/plots/PT_82MX6J77-TMB-barplot.pdf\

[1] 15
[1] \/home/rstudio/pbta-tumor-evolution/CHOP/GitHub/pbta-tumor-evolution/analyses/tmb-vaf-longitudinal/plots/PT_89XRZBSG-TMB-barplot.pdf\

[1] 16
[1] \/home/rstudio/pbta-tumor-evolution/CHOP/GitHub/pbta-tumor-evolution/analyses/tmb-vaf-longitudinal/plots/PT_8GN3TQRM-TMB-barplot.pdf\

[1] 17
[1] \/home/rstudio/pbta-tumor-evolution/CHOP/GitHub/pbta-tumor-evolution/analyses/tmb-vaf-longitudinal/plots/PT_962TCBVR-TMB-barplot.pdf\

[1] 18
[1] \/home/rstudio/pbta-tumor-evolution/CHOP/GitHub/pbta-tumor-evolution/analyses/tmb-vaf-longitudinal/plots/PT_98QMQZY7-TMB-barplot.pdf\

[1] 19
[1] \/home/rstudio/pbta-tumor-evolution/CHOP/GitHub/pbta-tumor-evolution/analyses/tmb-vaf-longitudinal/plots/PT_99S5BPE3-TMB-barplot.pdf\

[1] 20
[1] \/home/rstudio/pbta-tumor-evolution/CHOP/GitHub/pbta-tumor-evolution/analyses/tmb-vaf-longitudinal/plots/PT_9PJR0ZK7-TMB-barplot.pdf\

[1] 21
[1] \/home/rstudio/pbta-tumor-evolution/CHOP/GitHub/pbta-tumor-evolution/analyses/tmb-vaf-longitudinal/plots/PT_9S6WMQ92-TMB-barplot.pdf\

[1] 22
[1] \/home/rstudio/pbta-tumor-evolution/CHOP/GitHub/pbta-tumor-evolution/analyses/tmb-vaf-longitudinal/plots/PT_AQWDQW27-TMB-barplot.pdf\

[1] 23
[1] \/home/rstudio/pbta-tumor-evolution/CHOP/GitHub/pbta-tumor-evolution/analyses/tmb-vaf-longitudinal/plots/PT_CXT81GRM-TMB-barplot.pdf\

[1] 24
[1] \/home/rstudio/pbta-tumor-evolution/CHOP/GitHub/pbta-tumor-evolution/analyses/tmb-vaf-longitudinal/plots/PT_DFQAH7RS-TMB-barplot.pdf\

[1] 25
[1] \/home/rstudio/pbta-tumor-evolution/CHOP/GitHub/pbta-tumor-evolution/analyses/tmb-vaf-longitudinal/plots/PT_ESHACWF6-TMB-barplot.pdf\

[1] 26
[1] \/home/rstudio/pbta-tumor-evolution/CHOP/GitHub/pbta-tumor-evolution/analyses/tmb-vaf-longitudinal/plots/PT_FN4GEEFR-TMB-barplot.pdf\

[1] 27
[1] \/home/rstudio/pbta-tumor-evolution/CHOP/GitHub/pbta-tumor-evolution/analyses/tmb-vaf-longitudinal/plots/PT_HFQNKP5X-TMB-barplot.pdf\

[1] 28
[1] \/home/rstudio/pbta-tumor-evolution/CHOP/GitHub/pbta-tumor-evolution/analyses/tmb-vaf-longitudinal/plots/PT_HJMP6PH2-TMB-barplot.pdf\

[1] 29
[1] \/home/rstudio/pbta-tumor-evolution/CHOP/GitHub/pbta-tumor-evolution/analyses/tmb-vaf-longitudinal/plots/PT_JNEV57VK-TMB-barplot.pdf\

[1] 30
[1] \/home/rstudio/pbta-tumor-evolution/CHOP/GitHub/pbta-tumor-evolution/analyses/tmb-vaf-longitudinal/plots/PT_JP1FDKN9-TMB-barplot.pdf\

[1] 31
[1] \/home/rstudio/pbta-tumor-evolution/CHOP/GitHub/pbta-tumor-evolution/analyses/tmb-vaf-longitudinal/plots/PT_JSFBMK5V-TMB-barplot.pdf\

[1] 32
[1] \/home/rstudio/pbta-tumor-evolution/CHOP/GitHub/pbta-tumor-evolution/analyses/tmb-vaf-longitudinal/plots/PT_K8ZV7APT-TMB-barplot.pdf\

[1] 33
[1] \/home/rstudio/pbta-tumor-evolution/CHOP/GitHub/pbta-tumor-evolution/analyses/tmb-vaf-longitudinal/plots/PT_KMHGNCNR-TMB-barplot.pdf\

[1] 34
[1] \/home/rstudio/pbta-tumor-evolution/CHOP/GitHub/pbta-tumor-evolution/analyses/tmb-vaf-longitudinal/plots/PT_MDWPRDBT-TMB-barplot.pdf\

[1] 35
[1] \/home/rstudio/pbta-tumor-evolution/CHOP/GitHub/pbta-tumor-evolution/analyses/tmb-vaf-longitudinal/plots/PT_MNSEJCDM-TMB-barplot.pdf\

[1] 36
[1] \/home/rstudio/pbta-tumor-evolution/CHOP/GitHub/pbta-tumor-evolution/analyses/tmb-vaf-longitudinal/plots/PT_N8W26H19-TMB-barplot.pdf\

[1] 37
[1] \/home/rstudio/pbta-tumor-evolution/CHOP/GitHub/pbta-tumor-evolution/analyses/tmb-vaf-longitudinal/plots/PT_NPETR8RY-TMB-barplot.pdf\

[1] 38
[1] \/home/rstudio/pbta-tumor-evolution/CHOP/GitHub/pbta-tumor-evolution/analyses/tmb-vaf-longitudinal/plots/PT_PFA762TK-TMB-barplot.pdf\

[1] 39
[1] \/home/rstudio/pbta-tumor-evolution/CHOP/GitHub/pbta-tumor-evolution/analyses/tmb-vaf-longitudinal/plots/PT_PR4YBBH3-TMB-barplot.pdf\

[1] 40
[1] \/home/rstudio/pbta-tumor-evolution/CHOP/GitHub/pbta-tumor-evolution/analyses/tmb-vaf-longitudinal/plots/PT_QH9H491G-TMB-barplot.pdf\

[1] 41
[1] \/home/rstudio/pbta-tumor-evolution/CHOP/GitHub/pbta-tumor-evolution/analyses/tmb-vaf-longitudinal/plots/PT_RJ1TJ2KH-TMB-barplot.pdf\

[1] 42
[1] \/home/rstudio/pbta-tumor-evolution/CHOP/GitHub/pbta-tumor-evolution/analyses/tmb-vaf-longitudinal/plots/PT_S2SQJVGK-TMB-barplot.pdf\

[1] 43
[1] \/home/rstudio/pbta-tumor-evolution/CHOP/GitHub/pbta-tumor-evolution/analyses/tmb-vaf-longitudinal/plots/PT_S4YNE17X-TMB-barplot.pdf\

[1] 44
[1] \/home/rstudio/pbta-tumor-evolution/CHOP/GitHub/pbta-tumor-evolution/analyses/tmb-vaf-longitudinal/plots/PT_T2M1338J-TMB-barplot.pdf\

[1] 45
[1] \/home/rstudio/pbta-tumor-evolution/CHOP/GitHub/pbta-tumor-evolution/analyses/tmb-vaf-longitudinal/plots/PT_TKWTTRQ7-TMB-barplot.pdf\

[1] 46
[1] \/home/rstudio/pbta-tumor-evolution/CHOP/GitHub/pbta-tumor-evolution/analyses/tmb-vaf-longitudinal/plots/PT_W6AWJJK7-TMB-barplot.pdf\

[1] 47
[1] \/home/rstudio/pbta-tumor-evolution/CHOP/GitHub/pbta-tumor-evolution/analyses/tmb-vaf-longitudinal/plots/PT_WP871F5S-TMB-barplot.pdf\

[1] 48
[1] \/home/rstudio/pbta-tumor-evolution/CHOP/GitHub/pbta-tumor-evolution/analyses/tmb-vaf-longitudinal/plots/PT_XA98HG1C-TMB-barplot.pdf\

[1] 49
[1] \/home/rstudio/pbta-tumor-evolution/CHOP/GitHub/pbta-tumor-evolution/analyses/tmb-vaf-longitudinal/plots/PT_XHYBZKCX-TMB-barplot.pdf\

[1] 50
[1] \/home/rstudio/pbta-tumor-evolution/CHOP/GitHub/pbta-tumor-evolution/analyses/tmb-vaf-longitudinal/plots/PT_XTVQB9S4-TMB-barplot.pdf\

[1] 51
[1] \/home/rstudio/pbta-tumor-evolution/CHOP/GitHub/pbta-tumor-evolution/analyses/tmb-vaf-longitudinal/plots/PT_YGN06RPZ-TMB-barplot.pdf\

[1] 52
[1] \/home/rstudio/pbta-tumor-evolution/CHOP/GitHub/pbta-tumor-evolution/analyses/tmb-vaf-longitudinal/plots/PT_Z4GS3ZQQ-TMB-barplot.pdf\

[1] 53
[1] \/home/rstudio/pbta-tumor-evolution/CHOP/GitHub/pbta-tumor-evolution/analyses/tmb-vaf-longitudinal/plots/PT_ZMKMKCFQ-TMB-barplot.pdf\

[1] 54
[1] \/home/rstudio/pbta-tumor-evolution/CHOP/GitHub/pbta-tumor-evolution/analyses/tmb-vaf-longitudinal/plots/PT_ZZRBX5JT-TMB-barplot.pdf\

sessionInfo()
R version 4.2.3 (2023-03-15)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: Ubuntu 22.04.2 LTS

Matrix products: default
BLAS:   /usr/lib/x86_64-linux-gnu/openblas-pthread/libblas.so.3
LAPACK: /usr/lib/x86_64-linux-gnu/openblas-pthread/libopenblasp-r0.3.20.so

locale:
 [1] LC_CTYPE=en_US.UTF-8       LC_NUMERIC=C              
 [3] LC_TIME=en_US.UTF-8        LC_COLLATE=en_US.UTF-8    
 [5] LC_MONETARY=en_US.UTF-8    LC_MESSAGES=en_US.UTF-8   
 [7] LC_PAPER=en_US.UTF-8       LC_NAME=C                 
 [9] LC_ADDRESS=C               LC_TELEPHONE=C            
[11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C       

attached base packages:
[1] grid      stats     graphics  grDevices utils     datasets  methods  
[8] base     

other attached packages:
 [1] ggthemes_4.2.4  lubridate_1.9.2 forcats_1.0.0   stringr_1.5.0  
 [5] dplyr_1.1.1     purrr_1.0.1     readr_2.1.4     tidyr_1.3.0    
 [9] tibble_3.2.1    ggplot2_3.4.0   tidyverse_2.0.0

loaded via a namespace (and not attached):
 [1] highr_0.10       bslib_0.4.2      compiler_4.2.3   pillar_1.9.0    
 [5] jquerylib_0.1.4  tools_4.2.3      bit_4.0.5        digest_0.6.31   
 [9] timechange_0.2.0 jsonlite_1.8.4   evaluate_0.20    lifecycle_1.0.3 
[13] gtable_0.3.3     pkgconfig_2.0.3  rlang_1.1.0      cli_3.6.1       
[17] parallel_4.2.3   yaml_2.3.7       xfun_0.38        fastmap_1.1.1   
[21] withr_2.5.0      knitr_1.42       generics_0.1.3   vctrs_0.6.2     
[25] sass_0.4.5       hms_1.1.3        bit64_4.0.5      rprojroot_2.0.3 
[29] tidyselect_1.2.0 glue_1.6.2       R6_2.5.1         fansi_1.0.4     
[33] vroom_1.6.1      rmarkdown_2.21   farver_2.1.1     tzdb_0.3.0      
[37] magrittr_2.0.3   scales_1.2.1     htmltools_0.5.5  colorspace_2.1-0
[41] labeling_0.4.2   utf8_1.2.3       stringi_1.7.12   munsell_0.5.0   
[45] cachem_1.0.7     crayon_1.5.2    
---
title: "Explore TMB and number of mutations across multiple timepoints of the PBTA Cohort"
author: "Antonia Chroni <chronia@chop.edu> for D3B"
date: "2023"
output:
  html_notebook:
    toc: TRUE
    toc_float: TRUE
---

#### Tumor evolution project 

### Data used 
In this notebook, we are using the `tmb_genomic.tsv` file generated from the `01-preprocess-data.Rmd` script.

# Set up
```{r load-library}
suppressPackageStartupMessages({
  library(tidyverse)
})
```

# Directories and File Inputs/Outputs
```{r set-dir-and-file-names}
# Detect the ".git" folder. This will be in the project root directory.
# Use this as the root directory to ensure proper sourcing of functions
# no matter where this is called from.
root_dir <- rprojroot::find_root(rprojroot::has_dir(".git"))
scratch_dir <- file.path(root_dir, "scratch")
analysis_dir <- file.path(root_dir, "analyses", "tmb-vaf-longitudinal") 
input_dir <- file.path(analysis_dir, "input")

# Input files
tmb_genomic_file <- file.path(scratch_dir, "tmb_genomic.tsv")
palette_file <- file.path(root_dir, "figures", "palettes", "tumor_descriptor_color_palette.tsv")

# File path to plots directory
plots_dir <-
  file.path(analysis_dir, "plots")
if (!dir.exists(plots_dir)) {
  dir.create(plots_dir)
}

source(paste0(analysis_dir, "/util/function-create-barplot.R"))
source(paste0(analysis_dir, "/util/function-create-dumbbell-plot.R"))
source(paste0(root_dir, "/figures/scripts/theme.R"))
```

# Read in data and process
```{r read_input_files}
# Read and process tmb_genomic file
df_total <- readr::read_tsv(tmb_genomic_file, guess_max = 100000, show_col_types = FALSE) 

# Are there any samples with both WGS and WXS? 
df_total %>% 
  unique() %>% 
  arrange(Kids_First_Participant_ID, experimental_strategy)  %>%
  group_by(Kids_First_Participant_ID) %>%
  dplyr::summarise(experimental_strategy_sum = str_c(experimental_strategy, collapse = ";")) 

# There are, so let's remove these from downstream analyses.
df <- df_total %>% 
  filter(!experimental_strategy == "WXS") %>% 
  dplyr:::mutate(patient_id = paste(short_histology, Kids_First_Participant_ID, sep = "_"))
    
# Read color palette
palette_df <- readr::read_tsv(palette_file, guess_max = 100000, show_col_types = FALSE)
```

# TMB per Patient case
We will explore TMB per `Kids_First_Participant_ID` over time by creating stacked barplots.

```{r create-stacked-barplot, fig.width = 15, fig.height = 6, fig.fullwidth = TRUE}
# Define parameters for function
ylim = max(df$tmb)

# df
f <- c("Second Malignancy", "Unavailable", "Deceased", "Recurrence", "Progressive", "Diagnosis") # Level df by timepoints
df_plot <- df %>% 
  dplyr:::mutate(tumor_descriptor = factor(tumor_descriptor),
                 tumor_descriptor = fct_relevel(tumor_descriptor, f)) 

# Run function
fname <- paste0(plots_dir, "/", "TMB-genomic-total.pdf")
print(fname)
p <- create_stacked_barplot(tmb_df = df_plot, ylim = ylim)
pdf(file = fname, width = 15, height = 6)
print(p)
dev.off()
```
Attention: Hypermutant TMB defined as ≥10 Mb, and Ultrahypermutant TMB defined as ≥100 mutations/Mb (https://pubmed.ncbi.nlm.nih.gov/29056344/).

Here, we notice that there are samples with high TMB (hyper-mutant samples). Next, we will exclude these samples (threshold >= 10) from downstream analysis. Attention is needed in cases with high number of mutations in only one timepoint as this will lead to un-matched longitudinal samples. We will also remove those so we always have matched longitudinal samples.

```{r create-stacked-barplot-filter, fig.width = 15, fig.height = 8, fig.fullwidth = TRUE}
# Filter df
df_plot_filter <- df %>%
  filter(!tmb >= 10)  %>%
  unique() %>% 
  arrange(Kids_First_Participant_ID, tumor_descriptor) %>%
  group_by(Kids_First_Participant_ID) %>%
  dplyr::summarise(tumor_descriptor_sum = str_c(tumor_descriptor, collapse = ";")) %>% 
  filter(!tumor_descriptor_sum %in% c("Diagnosis", "Progressive", "Recurrence")) %>% 
  dplyr::left_join(df, by = c("Kids_First_Participant_ID", "tumor_descriptor_sum")) %>% 
  mutate(cancer_group_sum = ifelse(short_histology == "HGAT", "High-grade glioma",
                                   ifelse(short_histology == "LGAT", "Low-grade glioma", "Other cancer group")),
         cancer_group_sum = replace_na(cancer_group_sum, "Other"),
         tumor_descriptor = factor(tumor_descriptor),
         tumor_descriptor = fct_relevel(tumor_descriptor, f)) %>% 
  drop_na(tmb) 


# Define parameters for function
ylim = max(df_plot_filter$tmb)
df_plot_filter <- df_plot_filter

# Run function
fname <- paste0(plots_dir, "/", "TMB-genomic-no-hypermutants.pdf")
print(fname)
p <- create_stacked_barplot(tmb_df = df_plot_filter, ylim = ylim)
pdf(file = fname, width = 25, height = 8)
print(p)
dev.off()
```

# TMB across timepoints and cancer types per Patient case
We will explore TMB per cancer group over time by creating dumbbell plots. We classified by using cancer types with the highest number of samples (High- and Low-grade gliomas) versus any other cancer groups.

```{r create-dumbbell-ct, fig.width = 18, fig.height = 10, fig.fullwidth = TRUE}
cancer_groups <- unique(as.character(df_plot_filter$cancer_group_sum))
cancer_groups <- sort(cancer_groups, decreasing = FALSE)
print(cancer_groups)

for (i in seq_along(cancer_groups)) {
  print(i)
  df_ct_sub <- df_plot_filter %>% 
    filter(cancer_group_sum == cancer_groups [i])
  
  if (i == 1) {
    print(cancer_groups [i])
    # Define parameters for function
    ylim <- 8
    } else if (i == 2) {
      print(cancer_groups [i])
      # Define parameters for function
      ylim <- 4
      } else {
        print(cancer_groups [i])
        # Define parameters for function
        ylim <- 4
      }
    
    # Name plots
    fname <- paste0(plots_dir, "/", "TMB-genomic-dumbbell", "-", cancer_groups[i], ".pdf")
    print(fname)
    
    # Run function
    p <- create_dumbbell_ct(tmb_df = df_ct_sub, 
                                 ylim = ylim, 
                                 ct_id = cancer_groups[i])
    pdf(file = fname, width = 18, height = 10)
    print(p)
    dev.off()
}
```

# Total number of mutations across timepoints and cancer types per Patient case

```{r create-dumbbell-ct-mut, fig.width = 18, fig.height = 10, fig.fullwidth = TRUE}
for (i in seq_along(cancer_groups)) {
  print(i)
  df_ct_sub <- df_plot_filter %>% 
    filter(cancer_group_sum == cancer_groups [i])
  
  if (i == 1) {
    print(cancer_groups [i])
    # Define parameters for function
    ylim <- 260
    } else if (i == 2) {
      print(cancer_groups [i])
      # Define parameters for function
      ylim <- 150
      } else {
        print(cancer_groups [i])
        # Define parameters for function
        ylim <- 150
      }
    
    # Name plots
    fname <- paste0(plots_dir, "/", "Mutations-genomic-dumbbell", "-", cancer_groups[i], ".pdf")
    print(fname)
    
    # Run function
    p <- create_dumbbell_ct_mut(tmb_df = df_ct_sub, 
                                 ylim = ylim, 
                                 ct_id = cancer_groups[i])
    pdf(file = fname, width = 18, height = 10)
    print(p)
    dev.off()
}
```

# Total number of mutations across timepoints and biospecimen sample per Patient case
Here, we want to explore the number of mutations per timepoint and biospecimen sample per patient case.

```{r create-barplot-sample, fig.width = 5, fig.height = 4, fig.fullwidth = TRUE}
samples <- unique(as.character(df_plot_filter$Kids_First_Participant_ID))
print(samples)

for (i in seq_along(samples)) {
  print(i)
  tmb_sub <- df_plot_filter %>%
    filter(Kids_First_Participant_ID == samples[i])
  
  # Define parameters for function
  ylim <- 260
 
  # Run function
  fname <- paste0(plots_dir, "/", samples[i], "-TMB-barplot.pdf")
  print(fname)
  p <- create_barplot_sample(tmb_df = tmb_sub,
                             ylim = ylim,
                             sid = samples[i])
  pdf(file = fname, width = 5, height = 4)
  print(p)
  dev.off()
}
```

```{r echo=TRUE}
sessionInfo()
```
